Mota-Furtado, F. and O'Mahony, P. F. (2007) Exact propagator for generalized Ornstein-Uhlenbeck processes. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 75 (4).
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A closed form expression for the propagator is derived, in terms of modified Bessel functions, for the Fokker-Planck equation for a physically important generalization of the Ornstein-Uhlenbeck process where the diffusion constant D(p) is a function of the momentum. The closed form is found for the general case D(p)similar to vertical bar p vertical bar(-alpha) where alpha >= 0 and leads to the standard Gaussian form for alpha=0. The propagator for the specific case D(p)similar to vertical bar p vertical bar(-1) is used to derive analytic expressions for probability distributions and correlation coefficients. An exact expression is found for the constant of proportionality for the anomalous diffusion of the mean-square displacement of a particle at short times.
This is a Submitted version This version's date is: 4/2007 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/b4a9812f-58ab-e550-80ef-ffe4313207c5/9/
Deposited by Research Information System (atira) on 18-Nov-2014 in Royal Holloway Research Online.Last modified on 18-Nov-2014